Differentiable physics-enabled closure modeling for Burgers' turbulence

Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for Burgers' turbulence. We consider the one-dimensional Burgers system as a prototypical test problem for modeling the unresolved terms in advection-dominated turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an a posteriori loss function to test the efficacy of models across a range of system parameters, including viscosity, time, and grid resolution. We find that constraining models with inductive biases in the form of partial differential equations that contain known physics or existing closure approaches produces highly data-efficient, accurate, and generalizable models, outperforming state-of-the-art baselines. Addition of structure in the form of physics information also brings a level of interpretability to the models, potentially offering a stepping stone to the future of closure modeling.

Automated summary

Data-driven turbulence modeling is gaining attention with advancements in the data sciences. By combining known physics with machine learning, we present an approach using differentiable physics paradigm to develop closure models for Burgers' turbulence. Our study focuses on the one-dimensional Burgers system as a test case for modeling unresolved terms in advection-dominated turbulence problems. Through training models with various physical assumptions and evaluating their performance across different system parameters, we demonstrate that models constrained with inductive biases and partial differential equations outperform existing baselines in terms of efficiency, accuracy, and generalizability. Adding physics information also enhances interpretability and holds potential for the future of closure modeling.